Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration

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dc.citation.articleNumber154107en_US
dc.citation.issueNumber15en_US
dc.citation.journalTitleThe Journal of Chemical Physicsen_US
dc.citation.volumeNumber139en_US
dc.contributor.authorCui, Yaoen_US
dc.contributor.authorBulik, Ireneusz W.en_US
dc.contributor.authorJiménez-Hoyos, Carlos A.en_US
dc.contributor.authorHenderson, Thomas M.en_US
dc.contributor.authorScuseria, Gustavo E.en_US
dc.date.accessioned2017-05-04T19:43:54Zen_US
dc.date.available2017-05-04T19:43:54Zen_US
dc.date.issued2013en_US
dc.description.abstractWe study the spectra of the molecular orbital Hessian (stability matrix) and random-phase approximation (RPA) Hamiltonian of broken-symmetry Hartree-Fock solutions, focusing on zero eigenvalue modes. After all negative eigenvalues are removed from the Hessian by following their eigenvectors downhill, one is left with only positive and zero eigenvalues. Zero modes correspond to orbital rotations with no restoring force. These rotations determine states in the Goldstone manifold, which originates from a spontaneously broken continuous symmetry in the wave function. Zero modes can be classified as improper or proper according to their different mathematical and physical properties. Improper modes arise from symmetry breaking and their restoration always lowers the energy. Proper modes, on the other hand, correspond to degeneracies of the wave function, and their symmetry restoration does not necessarily lower the energy. We discuss how the RPA Hamiltonian distinguishes between proper and improper modes by doubling the number of zero eigenvalues associated with the latter. Proper modes in the Hessian always appear in pairs which do not double in RPA. We present several pedagogical cases exemplifying the above statements. The relevance of these results for projected Hartree-Fock methods is also addressed.en_US
dc.identifier.citationCui, Yao, Bulik, Ireneusz W., Jiménez-Hoyos, Carlos A., et al.. "Proper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restoration." <i>The Journal of Chemical Physics,</i> 139, no. 15 (2013) American Institute of Physics: https://doi.org/10.1063/1.4824905.en_US
dc.identifier.doihttps://doi.org/10.1063/1.4824905en_US
dc.identifier.urihttps://hdl.handle.net/1911/94176en_US
dc.language.isoengen_US
dc.publisherAmerican Institute of Physicsen_US
dc.rightsArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.en_US
dc.titleProper and improper zero energy modes in Hartree-Fock theory and their relevance for symmetry breaking and restorationen_US
dc.typeJournal articleen_US
dc.type.dcmiTexten_US
dc.type.publicationpublisher versionen_US
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